Mathematical Sciences: Sklyanin Algebras & Graded Algebras

史密斯 主要研究者将研究的是，noetherian分次代数，特别是Sklyanin代数。 这些代数的研究在非交换代数几何的发展中具有重要意义。 一个关键问题是对Sklyanin代数上的胖点模进行分类。 首席研究员还将扩大到更高的维度的结果，他已经获得了4维Sklyanin代数。 此外，非交换曲面的Gelfand-Kirillov维3将进行研究。 这将提供一个更清楚的了解一般轮廓的非交换代数几何。 这项研究是在非交换环理论的一般领域。 该项目中考虑的环在许多数学领域，包括代数几何中都很有意义。 给定一条曲线，其中一个环可以与曲线上的某些点相关联。 更好地理解这些环和这种关联将有助于确定给定曲线的几何形状。***

Smith The principal investigator will study finitely presented, noetherian graded algebras, particularly the Sklyanin algebras. The study of these algebras has been significant in the development of noncommutative algebraic geometry. A key problem is to classify the fat point modules over the Sklyanin algebras. The principal investigator will also extend to higher dimensions the results he has obtained on the 4-dimensional Sklyanin algebras. In addition, noncommutative surfaces of Gelfand-Kirillov dimension 3 will be studied. This will provide a clearer understanding of the general outline of noncommutative algebraic geometry. This research is in the general area of noncommutative ring theory. The rings considered in the project are of interest in many areas of mathematics including algebraic geometry. Given a curve, one of these rings can be associated with certain points on the curve. A better understanding of these rings and this association will be useful in determine the geometry of a given curve. ***